Algebraically closed field
Positive Impact Program Evaluation
... We must have [R( a + bi ) ∶ R] = 2. Therefore the minimal polynomial of a + bi has a − bi as a zero as well. Thus, we must have ( x − ( a + bi ))( x − ( a − bi )) ∈ ker ( ϕ ) = m. Hence, m corresponds to a conjugate pair ...
58
Block algebras with HH1 a simple Lie algebra
... Abstract. The purpose of this note is to add to the evidence that the algebra structure of a p-block of a finite group is closely related to the Lie algebra structure of its first Hochschild cohomology group. We show ...
6
Modules over group algebras which are free on restriction to a maximal subgroup
... an algebraically closed field of characteristic p and G will be a finite p-group, V will be a non-projective, indecomposable kG-module which is free on restriction to some maximal subgroup of ...
216
Irreducible Representations of Algebraic Group SL(6,K) in charK =3
... an algebraically closed field K of characteristic 2 in [7] [8] and for the special orthogonal group SO ( 6, K ) and the symplectic group Sp ( 6, K ) over an algebraically closed ...
11
Irreducible characters of the unitriangular group and coadjoint orbits
... an algebraically closed field of prime characteristic ...a closed subgroup of some unitriangular group (see [Hul; corollary ...a closed subgoup of some ...arbitrary field K. In ...
262
On the Classification of k-involutions of SL(n,k) and O(n,k) over Fields of Characteristic 2.
... Proof. For the first two cases, there is exactly one square class, so conjugation by a matrix A is equivalent to conjugation by the identity matrix. In other words, A is congruent to the identity matrix. For the last ...
85
Algebraic Envelope of Groups and their Properties
... Algebraic Envelope of the Group of Integers We know that for abelian affine groups over an algebraically closed field, the exact sequence i#.. As one would expect, the algebraic envelope[r] ...
92
The slice method for G torsors
... In section 4 we saw how to construct a slice of a geometrically irreducible G-variety, when an SGP exists. This may not always be the case, especially for actions of non-reductive groups. So we give another construction ...
23
Unipotent subgroups of reductive algebraic groups
... 3.3.1 Let G be a connected semisimple algebraic group of adjoint type defined over Suppose we have established the MT for an algebraically closed field of characteristic p>0... simple ad[r] ...
146
D affinity and rational varieties
... Our main result is that a D-affine rational projective surface over an algebraically closed field is a generalised flag variety of a reductive group... Let us consider a connected smooth[r] ...
10
On semi modular subalgebras of Lie algebras over fields of arbitrary characteristic
... perfect field of char- acteristic three which has a sm subalgebra that is not ...an algebraically closed field of characteristic p > 0 that have absolute toral rank ≤ 1 or are restricted, ...
14
Branched Covers of Curves With Fixed Ramification Locus
... an algebraically closed field k of fixed degree and fixed ramification locus, under a notion of equivalence derived from considering linear series on a fixed source curve ...
104
Reducible subgroups of exceptional algebraic groups
... an algebraically closed field. Following [25], a closed subgroup H of G is said to be G-completely reducible (G-cr) if whenever H is contained in a parabolic subgroup P of G, it is contained ...
48
Commuting Involutions of SL(n,k)
... an algebraically closed field being given by an index (related to the associated root system of G), the actions of the Galois group Γ of K/k where for G a reductive k-group, T a maximal k-torus of G, ...
144
On the continuous part of codimension two algebraic cycles on threefolds over a field
... Let X be a non-singular projective threeefold over an algebraically closed field k satisfying the assumptions of Theorem 1. The below proof can be divided into two parts - chain of reductions and ...
16
Some results on Kähler modules
... Abstract: Let k be an algebraically closed field of characteristic zero, R, S affine k-algebras and letΩ(q)(R/k) and Ω(q)(S/k) denote their universal finite Kähler modules of d[r] ...
7
Isomorphy Classes of Involutions of SO(n,k,ß) and SP(2n,k) where n > 2.
... an algebraically closed field or the real numbers, and we have partial results for the finite prime fields and the p-adic ...over algebraically closed fields, the real numbers, and for ...
109
On nilpotent Lie algebras of derivations with large center
... Let K be an algebraically closed field of characteristic zero, and A be an associative commutative algebra over K with identity, without zero divisors. A K -linear mapping D : A −→ A is called K ...
10
Lifting Problems and Their Independence of the Coefficient Field
... function field K is given by the set of valuations of K that are trivial on the subfield ...function field in one variable over k, there is a unique curve with function field K, up to a unique ...
66
On projective and injective polynomial modules
... We work with a quantum general linear group over an arbitrary base field with arbitrary parameter q. We do this not only in the interests of generality but also because our results, which are new even in the ...
38